Deformations of Margulis space-times with parabolics
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913421102940160 |
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| author | Choi, Suhyoung |
| author_facet | Choi, Suhyoung |
| contents | Let $E$ be a flat Lorentzian space of signature $(2, 1)$. A Margulis space-time is a noncompact complete Lorentz flat $3$-manifold $E/Γ$ with a free isometry group $Γ$ of rank $g \geq 2$. We consider the case when $Γ$ contains a parabolic element. We show that sufficiently small deformations of $Γ$ still act properly on $E$. We use our previous work showing that $E/Γ$ can be compactified relative to a union of solid tori and some old idea of Carrière in his famous work. We will show that the there is also a decomposition of $E/Γ$ by crooked planes that are disjoint and embedded in a generalized sense. These can be perturbed so that $E/Γ$ decomposes into cells. This partially affirms the conjecture of Charette-Drumm-Goldman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformations of Margulis space-times with parabolics Choi, Suhyoung Geometric Topology 57M50, 83A99 Let $E$ be a flat Lorentzian space of signature $(2, 1)$. A Margulis space-time is a noncompact complete Lorentz flat $3$-manifold $E/Γ$ with a free isometry group $Γ$ of rank $g \geq 2$. We consider the case when $Γ$ contains a parabolic element. We show that sufficiently small deformations of $Γ$ still act properly on $E$. We use our previous work showing that $E/Γ$ can be compactified relative to a union of solid tori and some old idea of Carrière in his famous work. We will show that the there is also a decomposition of $E/Γ$ by crooked planes that are disjoint and embedded in a generalized sense. These can be perturbed so that $E/Γ$ decomposes into cells. This partially affirms the conjecture of Charette-Drumm-Goldman. |
| title | Deformations of Margulis space-times with parabolics |
| topic | Geometric Topology 57M50, 83A99 |
| url | https://arxiv.org/abs/2407.05932 |